Calculate to three significant digits the density of carbon monoxide gas at exactly 25∘C and exactly 1 atm. You can assume carbon monoxide gas
Answer
🧪 Density of Carbon Monoxide (CO) Gas
Objective:
To calculate the density of carbon monoxide (CO) gas at:
- Temperature: 25.0 °C
- Pressure: 1.00 atm
Assume ideal gas behavior.
Step 1: Use the Ideal Gas Law in Terms of Density
Start from the ideal gas law:
PV = nRT
Using the relation n = m / M:
PV = (m / M) × RT ⇒ ρ = m / V = PM / RT
Thus, the formula becomes:
ρ = (PM) / (RT)
Step 2: Known Values
- P = 1.00 atm
- T = 25.0 °C = 298.15 K
- R = 0.0821 L·atm/(mol·K)
- M (molar mass of CO) = 28.01 g/mol
Step 3: Substitute and Calculate
ρ = (1.00 × 28.01) / (0.0821 × 298.15)
ρ = 28.01 / 24.487215 ≈ 1.143 g/L
ρ = 28.01 / 24.487215 ≈ 1.143 g/L
✅ Final Answer:
ρ ≈ 1.14 g/L (rounded to three significant digits)
Concept Summary:
- Density increases with pressure and molar mass.
- Density decreases with increasing temperature.
- This equation is derived directly from the ideal gas law and applies to any ideal gas.